Foreign survivors of the Grenfell Tower disaster should be given a “full immigration amnesty” to encourage them to approach the authorities, Labour has said.

The party said the Home Office’s offer to let those directly affected by the fire stay in the UK for 12 months regardless of their immigration status did not go far enough, leaving survivors and their relatives “frightened” of seeking help.

The grace period was announced as the Government said it was sending in a specialist taskforce to help run the beleaguered Kensington and Chelsea council. The independent group will assist with the long-term recovery of the area after the council came under fierce criticism over its response to the disaster.

On Wednesday police said they had recovered the “last of the visible human remains” from the tower where teams have been meticulously sifting through tonnes of debris.

Metropolitan Police Commander Stuart Cundy said “87 recoveries” had been made in the three weeks since fire ripped through the high-rise block, but stressed “the catastrophic damage” inside meant “that is not 87 people”.

So far 21 bodies have been formally identified by the coroner and their families informed. Mr Cundy said there were still 23 flats where investigators have been unable to trace or speak to anyone who was in those properties on the night.

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Police assume that no-one from any of those flats survived, although they are unable to say with certainty how many people may have been in those flats, either as occupiers or visitors, until the search is complete.

On Wednesday Home Office minister Brandon Lewis said foreigners directly affected by the fire will be allowed to stay in the UK for 12 months regardless of their immigration status so they can “deal with the extremely difficult circumstances”.

In a written statement to Parliament he said the Government’s priority is “to ensure that victims of this tragedy get the access they need to vital services, irrespective of immigration status”. Mr Lewis said the period of leave will help them to “start to rebuild their lives whilst considering their future options, as well as to assist the police and other authorities with their inquiries about the fire”.

The Home Office had already said it would not conduct immigration checks on survivors and those coming forward with information.

However shadow home secretary Diane Abbott said the “partial measure” does not go far enough and urged the Government to give survivors or their family members indefinite leave to remain.

In a letter to Home Secretary Amber Rudd, she said: “Without a full immigration amnesty there will be survivors and relatives of survivors who are frightened to approach the authorities.

“There will be people who have died whom we will never know about, and too many people who need help whom will not receive it.”

On Wednesday Communities Secretary, Sajid Javid, announced an independent Recovery Taskforce would assist the council with the longer term recovery of the area.